Understanding Gravity at Long Distances

The star next to Sun does not have much gravitational influence on it. If it would have any influence it would have been felt by planets also. My questions are,

1. Then how do stars in a constellation stay together when they possibly cannot influence each other 'much' because of the huge distance between them?

2. How do clusters of galaxies form when there are utterly enormous distances between them?

In other words, the stars that are at the boundary of a galaxy do not have any 'power' to influence the boundary stars of a galaxy that is very very far away from them. So how do galaxies interact with each other?

Welcome to PF;
I can try to provide simple answers but sometimes more complex answers are easier to understand.
Bear in mind that "a simple curiosity" is what got the likes of Galileo into so much trouble.

The star next to Sun does not have much gravitational influence on it. If it would have any influence it would have been felt by planets also.

The size of the effect of alpha centauri on the solar system is only small in comparison with other effects much closer. In general, the motion of each star in the Milky Way is broadly determined by the overall distribution of the other stars. All those little effects add up.

1. Then how do stars in a constellation stay together when they possibly cannot influence each other 'much' because of the huge distance between them?

There is nothing special holding constellations together.

The constellations are just patterns that our mind sees in the sky. There is no special relationship between the stars that holds them in their constellations and the patterns will change over time as different stars are moving at different speeds.

2. How do clusters of galaxies form when there are utterly enormous distances between them?

There are also extremely large masses involved, and not much else to interact with.
The gravitational attraction only needs to be bigger than whatelse is out there ... which would be: other galactic clusters and cosmological expansion.

Consider an analogy -
You can have small eddies in a large whirlpool.
The overall flow of the whirlpool does not affect the motion of a bit of water in an eddy about the center of the eddy ... but it does act to keep lots of little eddies moving together about the center of the whirlpool.

1. Then how do stars in a constellation stay together when they possibly cannot influence each other 'much' because of the huge distance between them?

They are not staying together. They are moving in random directions, but the absolutely vast distances between us and the other stars mean that you can only see this movement with very very accurate instruments or over very long periods of time. Only after 100's to 1000's of years would there be any perceptible change in the constellations that you could see with the naked eye.

Plus, as Simon said, practically no stars in a constellation are gravitationally bound to each other. It's kind of like looking into a field full of fireflies that all light up at the same time. From your point of view some fireflies LOOK closer to others, but in reality they could be separated by the entire field.

2. How do clusters of galaxies form when there are utterly enormous distances between them?

Lots of gravity added up over LONG LONG LONG periods of time.

In other words, the stars that are at the boundary of a galaxy do not have any 'power' to influence the boundary stars of a galaxy that is very very far away from them. So how do galaxies interact with each other?

Sure they do. Gravitation has no limit in range. The stars on the boundary of a galaxy influence everything else in the universe. It's just that the further away the stars are from an object, the less their gravity influences them.

The star next to Sun does not have much gravitational influence on it. If it would have any influence it would have been felt by planets also. My questions are,

Ah, but it does have some. And this is felt by the planets also. The galaxy is held together by gravity, and yes, this force is very weak compared to the gravity we feel from the Earth. As Drakkith said, the galaxy forms over a very long time. And similarly the density of the galaxy is very small (compared to what we are used to here on Earth). In a way, you can think of the galactic gravity as happening on a completely different scale than the solar gravity. It is the same mechanism (gravity), but on different scales.

You can broadly say that every two masses in the Universe will be interacting, gravitationally. In each case, it's just a matter of scale. The effect of one galaxy on another is very small - just enough to deviate their paths by a tiny amount. The Sun affects the paths of the Moon and the Earth, they also, mutually affect each other and a rock in orbit around the Moon will also be subject to Sun, Moon and Earth (and vice-versa, of course). The tight orbit of the rock around the Moon is because of the close proximity. If the rock were 150million km from an isolated Moon (same distance as from the Sun now), the 'year' would be tens of thousands of Earth years long.
The Inverse Square Law will give the right answer for describing what happens in most circumstances.

Staff: Mentor

Fun fact: the gravitational force between earth and pluto is weaker than the force between earth and Alpha Centauri, 4 light years away.
All objects in the solar system are pulled a bit towards Alpha Centauri (with ~10-13 cm/s2) - as the acceleration is nearly the same for all objects, we cannot measure this.

If you combine the gravitational effects from all stars (and other matter) in our galaxy, this is sufficient to keep our sun on a slow circular path - we need 250 million years per revolution!

Another fun fact, which knocks Astrology on the head: the gravitational force from the Midwife's mass is greater on a newly born baby than the gravitational force from any of the planets or nearby stars.

Sure they do. Gravitation has no limit in range. The stars on the boundary of a galaxy influence everything else in the universe. It's just that the further away the stars are from an object, the less their gravity influences them.

Does it mean that a star can influence another star in due course of time even if they are infinite distance apart?

1. Consider that the stars are not infinitely apart but are hugely apart. When viewed from the angle that gravity is just the curvature of space time, what kind of a curvature of space is in action when the stars are so much apart that the space between them extends to huge distances and is flat for all purposes and it takes even light gazzillions of years to travel between them? I think there would be no action between such stars even if we wait for gazillions of years to pass.

By the same reasoning, it seems to me that galaxies cannot influence each other significantly as to cluster together.

2. Suppose a galaxy has gravitational influence up to say 5 light years. To my mind, it cannot influence another galaxy that is say 10 light years away from it even if we consider that huge amount of time has passed. It's because the first galaxy cannot 'extend' its influence beyond 5 light years. A galaxy having 'Gravity that has no limit' would require that the galaxy has infinite mass, it seems.

Staff: Mentor

2. Suppose a galaxy has gravitational influence up to say 5 light years. To my mind, it cannot influence another galaxy that is say 10 light years away from it even if we consider that huge amount of time has passed. It's because the first galaxy cannot 'extend' its influence beyond 5 light years. A galaxy having 'Gravity that has no limit' would require that the galaxy has infinite mass, it seems.

There is no such distance cutoff and the force of gravity (classically, which is what we're talking about here) does extend out to infinity.

The gravitational force between two objects is given by ##F=\frac{Gm_1m_2}{r^2}## where ##G## is a constant, ##r## is the distance between them, and ##m_1##, ##m_2## are the masses. As ##r## increases, the force gets weaker, but it never disappears completely - even when both masses are finite.

2. Suppose a galaxy has gravitational influence up to say 5 light years. To my mind, it cannot influence another galaxy that is say 10 light years away from it even if we consider that huge amount of time has passed. It's because the first galaxy cannot 'extend' its influence beyond 5 light years. A galaxy having 'Gravity that has no limit' would require that the galaxy has infinite mass, it seems.

As Nugatory said, gravity does have no limit, even though it does get less with distance. If it helps, imagine the galactic cluster as some continuous object which has a coarse-grained density as a function of position. The density of this 'object' is great enough for gravity to hold it together. (Well, actually, only if we include the dark matter, but that is a different discussion). And by 'coarse-grained', I mean when we use a density that is averaged over nearby galaxies. If we used a 'true' density, then it would be a Dirac delta function at the position of each galaxy. The reason to coarse-grain is because it makes calculation simpler. Also, that way it gives an intuitive way to think about the galactic cluster, rather than as a bunch of Dirac-delta functions, which I think is where you are having trouble imagining how they can all hold each other together via gravity.

We only have (successful) classical models for gravity so far.
Quantum gravity is still a work in progress.
Therefore, all these answers have been in terms of classical theory.

Does it mean that a star can influence another star in due course of time even if they are infinite distance apart?

Define "infinite".

Extremely distant events will hit causality limits in general relativity: they are "over the horizon of the Universe" so to speak and their influence may never be felt here due to the cosmological expansion.

1. Consider that the stars are not infinitely apart but are hugely apart. When viewed from the angle that gravity is just the curvature of space time, what kind of a curvature of space is in action when the stars are so much apart that the space between them extends to huge distances and is flat for all purposes and it takes even light gazzillions of years to travel between them? I think there would be no action between such stars even if we wait for gazillions of years to pass.

You realize that "action" is a technical term in physics right?

Basically, there is nothing in GR to suggest that the kind of absolutely flat space-time you are thinking of exists. Spacetime that we see is, overall, very flat - but not absolutely flat. Gravity certainly acts across the entire universe that we know about.
That's roughly 46 billion ly radius (visible).

That "for all purposes" has limits to it - for all whose purposes? - there will be some purposes where the small curvature present is not sufficiently flat. Generally it is too much work to take account of every object in the Universe when we do our calculations so we make approximations in the hope that local events have an influence that far outweighs anything "out there". This is often, but not always, OK. In cosmology, for eg. you seldom get away with it.

By the same reasoning, it seems to me that galaxies cannot influence each other significantly as to cluster together.

And yet they do - so, either the consensus of physics for the last few decades is wrong and you are the first to notice or there is something wrong with the reasoning.

2. Suppose a galaxy has gravitational influence up to say 5 light years.

That would be a pointless supposition since galaxies do have gravitational influence many more than 5ly.
Our own galaxy, by itself, is 100-120,000ly across and held together by gravity - so the influence of gravity extends some 5 orders of magnitude farther than you would have anyone suppose.
You seem to be having trouble with the sorts of distances that are on the cosmological scale.

To my mind, it cannot influence another galaxy that is say 10 light years away from it even if we consider that huge amount of time has passed. It's because the first galaxy cannot 'extend' its influence beyond 5 light years. A galaxy having 'Gravity that has no limit' would require that the galaxy has infinite mass, it seems.

The current models for gravity account for the long-range effects well enough to be useful for modelling large scale structures like galactic clusters. I'm sorry that this seems impossible "to your mind" - it happens to be true.

As Nugatory said, gravity does have no limit, even though it does get less with distance. If it helps, imagine the galactic cluster as some continuous object which has a coarse-grained density as a function of position. The density of this 'object' is great enough for gravity to hold it together. (Well, actually, only if we include the dark matter, but that is a different discussion). And by 'coarse-grained', I mean when we use a density that is averaged over nearby galaxies. If we used a 'true' density, then it would be a Dirac delta function at the position of each galaxy. The reason to coarse-grain is because it makes calculation simpler. Also, that way it gives an intuitive way to think about the galactic cluster, rather than as a bunch of Dirac-delta functions, which I think is where you are having trouble imagining how they can all hold each other together via gravity.

It is often said that atom/matter is 99.9999999% empty. My questions are:

1. When Earth is hugely empty, how can it have gravity?

2. Gravity is negligible at the scale of sub-atomic matter. How do all these small effects of nucleons, electrons etc. (that make up matter) add up to form total gravitational field of the Earth? Are they really responsible for this gravity, when we say that they have wave nature associated with them?

It is often said that atom/matter is 99.9999999% empty. My questions are:

1. When Earth is hugely empty, how can it have gravity?

2. Gravity is negligible at the scale of sub-atomic matter. How do all these small effects of nucleons, electrons etc. (that make up matter) add up to form total gravitational field of the Earth? Are they really responsible for this gravity, when we say that they have wave nature associated with them?

1. it is as sophiecentaur said. The atom is mostly empty, but the bit that is not empty is extremely dense. Have you heard of a neutron star? that is what happens if you remove the empty space. very dense.
2. yes, if you add up all the matter of the nucleons and electrons in the entire earth, then it should add up to the known mass of the earth. (this is a simple calculation for a neutron star, its density is roughly the same as the density of an atomic nucleus). And yes, gravity is not (so far as we know) compatible with quantum physics. But mass is fairly well explained in quantum physics, so we can calculate the mass of a bunch of particles. And we can say that a very large bunch of particles produces a gravitational field that affects their overall motion. But on the other hand, exactly how gravity affects one particle (quantum-mechanically) is a bit... not well known at this point.

@Deepak: lots of very small things can add up to a very big effect.
You seem to be having a lot of trouble believing this. Is that the case?

A lot of the answers to your previous questions were about this - galaxies a long way apart have a small effect on each other, but there are lots of galaxies and lots of time for things to happen in so all those small effects add up to the big effects that we see. It is the same at any scale.
Gravity has a very small effect at the atomic scale in comparison with the other stuff that goes on there. But it does have an effect - there are lots of atoms and they all add up just like you can get to any number, however large, by repeatedly adding the same small increment.

Personally I would discourage the idea that matter is mostly empty space - it tends to mislead people into thinking weird stuff like that it should be possible to push two objects through each other. I'd point out that fishnets are mostly holes too, but that doesn't stop them catching fish. Matter is mostly electromagnetic field with some other fields thrown in for good measure.

I can see you are having fun with these questions, but are you paying attention to the answers? Have you learned anything?

I can see you are having fun with these questions, but are you paying attention to the answers? Have you learned anything?

I am not asking questions for the sake of fun but I really want to understand things. I surely am learning a lot.

I have heard that light takes millions of years to come from the core of the sun to its surface as the sun has huge density.

1. Then how come a photon can come out of the nucleus almost instantaneously, when nucleus is very very dense?

2. If we assume that gravity is ultimately made up of small discrete units (may be gravitons), how come these small units come out of a nucleus/black holes/neutron stars etc., when they themselves suck in everything ( in case of black holes).

I mean to say if light cannot escape from a black hole, how can gravity (either in discrete units or as waves) itself escape from such a huge amount of mass? It seems to be a wrong question but I just want to clarify things!

I am not asking questions for the sake of fun but I really want to understand things. I surely am learning a lot.

Well, it will help you learn better if we stop just spoon-feeding you answers, and start getting you to reason your way through to the answers yourself ... you seem to have the ability...

I have heard that light takes millions of years to come from the core of the sun to its surface as the sun has huge density.

Where from - when you hear something, it is useful to say where you heard it. I heard that the Sun went extinct a long time ago and the government is covering it up.

http://en.wikipedia.org/wiki/Solar_core
... according to that article, what are the factors that contribute to the time it takes for a photon to travel from the core to the surface? Is it just the density? Or is the overall size also important?

1. Then how come a photon can come out of the nucleus almost instantaneously, when nucleus is very very dense?

Considering the factors from your reading (above) - how does the relative size of the Sun compared with an atomic nucleus factor in to the time for a photon to emerge?

2. If we assume that gravity is ultimately made up of small discrete units (may be gravitons), how come these small units come out of a nucleus/black holes/neutron stars etc., when they themselves suck in everything ( in case of black holes).

Is a graviton usually considered to be a unit of gravity, or a particle that mediates the gravitational force?
What is the difference?

I mean to say if light cannot escape from a black hole, how can gravity (either in discrete units or as waves) itself escape from such a huge amount of mass? It seems to be a wrong question but I just want to clarify things!

That is something that a quantum theory of gravity has to explain :) we don't have one of those.
Why would a graviton experience gravity - it is gravity?

Anyway: We use general relativity instead - where gravity is described by a different mechanism.

@Deepak
If you want an answer to your question which involves Newton's ideas then you would not get an answer which is consistent with modern Cosmology. He assumed an infinite, stable universe without relativity or QM. So you can only get a partial answer in classical terms.

It can be counter productive to ask questions that pinpoint inconsistencies in our state of knowledge. Our knowledge is full of inconsistencies - that is a given and always will be. You can start by assuming an inverse square law but that must fall down when considering effects where the distances are of the order of c and the age of the Universe. All models have to involve a bit of a fudge in places - for instance, the conclusion that there must have been 'Inflation' in the period just after the Big Bang. That's really not aesthetically pleasing to brains that favour simple formulae with just three terms in them. But we're stuck with it - until a better (more pleasing or more accurate) idea comes along.
Your question:

I mean to say if light cannot escape from a black hole, how can gravity (either in discrete units or as waves) itself escape from such a huge amount of mass? It seems to be a wrong question but I just want to clarify things!

Would a satisfactory comment to this be that the formation of a black hole is essentially a slow process and the gravitational situation is part of the structure itself. EM radiation (the radiation we can detect, at least) involves quicker changes such as light or radio waves? (And we haven't yet detected gravitons, of course). One could possibly expect the situation to be different at very low frequencies. (In any case, Hawking Radiation is a predicted form of EM radiation that can 'escape' from black holes - so there is even a way out for EM energy)

@Deepak
If you want an answer to your question which involves Newton's ideas then you would not get an answer which is consistent with modern Cosmology. He assumed an infinite, stable universe without relativity or QM. So you can only get a partial answer in classical terms.

It can be counter productive to ask questions that pinpoint inconsistencies in our state of knowledge. Our knowledge is full of inconsistencies - that is a given and always will be. You can start by assuming an inverse square law but that must fall down when considering effects where the distances are of the order of c and the age of the Universe. All models have to involve a bit of a fudge in places - for instance, the conclusion that there must have been 'Inflation' in the period just after the Big Bang. That's really not aesthetically pleasing to brains that favour simple formulae with just three terms in them. But we're stuck with it - until a better (more pleasing or more accurate) idea comes along.
Your question:

Would a satisfactory comment to this be that the formation of a black hole is essentially a slow process and the gravitational situation is part of the structure itself. EM radiation (the radiation we can detect, at least) involves quicker changes such as light or radio waves? (And we haven't yet detected gravitons, of course). One could possibly expect the situation to be different at very low frequencies. (In any case, Hawking Radiation is a predicted form of EM radiation that can 'escape' from black holes - so there is even a way out for EM energy)

I do not always think about extreme cases in science but very simple scenarios.

Most of the people tell me that I am asking a 'why' question that is very difficult/impossible to answer. I reply that in many cases a why question can easily be changed to a how question. I give a few examples below:

1. Why inertia? can be changed to How is a body able to move for infinite time in the absence of any force?

2. Why are electrons all the same? can be changed to How is it that no electron differs from any other electron even if we consider gazillions of them?

3. Why this universe? can be changed to How is it that we have this universe instead of nothing?

The above 'how' questions do not deal in extremes but are very simple questions.

Similarly, when I ask that how can a nucleus/proton/nucleon/quark etc. that is extremely dense allow the emission of a photon, I am simply stating a curiosity, which I think cannot be counter-productive.

On the same lines I ask the following:

If we have a very huge concentration of electromagnetic 'energy', I suppose (may be wrongly, do correct me!) even that would not allow things to escape from it. Here, we don't need the usual concept of gravity, as matter is not involved.

So, it seems something else is the cause than gravity rather than just matter. BTW its just my imagination, which I think shouldn't be counter-productive even if it's wrong.